Why does the drag force increase with velocity and viscosity?

  • Context: Undergrad 
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Discussion Overview

The discussion focuses on the relationship between drag force, velocity, and viscosity, exploring why the exponent n in the drag force equation increases with these factors. Participants seek to understand the mathematical implications and general behavior of drag force across different speed ranges.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant states that the drag force is proportional to velocity raised to some power n, which increases with both velocity and viscosity.
  • Another participant suggests that n increases due to turbulence, noting the shape dependency of drag and questioning the meaningfulness of n in practical applications.
  • A different perspective highlights the importance of Reynolds number in understanding how the drag coefficient varies with velocity, suggesting that there are regions where the drag coefficient remains constant or varies in a specific manner.
  • A later reply indicates that the participant has researched Reynolds number further, acknowledging the complexity of the topic.

Areas of Agreement / Disagreement

Participants express differing views on the significance and behavior of the exponent n, with no consensus on its implications or the existence of universal formulas for n.

Contextual Notes

The discussion lacks clarity on the specific mathematical relationships and assumptions regarding the drag coefficient and its dependence on Reynolds number, as well as the conditions under which different behaviors are observed.

Who May Find This Useful

This discussion may be of interest to those studying fluid dynamics, particularly in relation to drag forces, turbulence, and the effects of viscosity on motion through fluids.

TMM
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I know that the drag force is proportional to the velocity to some power, n, and that n increases with velocity and with the viscosity of the medium.

I want to know why n increases, and how (mathematically) it increases. Some general speed ranges for v and v^2 in STP would be appreciated as well.
 
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n increases because turbulence increases.
The drag is so shape dependent, that I don't if there are formulas for n.
The fact that n depends on v means that n is really meaningless,
and is just used to make problems tractable
 
This sort of thing is usually discussed by specifying how the drag coefficient varies with Reynolds number (which depends on velocity). You should find some nice plots if you search for those terms. Although these can be complicated, there are large regions where the drag coefficient remains approximately constant (F ~ v^2) or goes like 1/R (so F ~ v).
 
Alright, I looked up some things on Reynolds number as you suggested.

Thanks for the info.
 

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